1. First Guess.
How close was your guess? Were you surprised by the actual value? In what way? How might you guess differently the next time?
Solution.
Results will vary.
Section 26.3 Applet Exploration: Correlation Guessing Game
Exercises Exploration Tasks
Using the Guess the Correlation applet (below or open in a new window).
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Leave the number of points set to 25 and press New Sample.
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The applet will display a scatterplot. Guess the value of the correlation coefficient in this scatterplot and enter this guess into the “Correlation guess” box.
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Then press the Check Guess button.
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Press the New Sample button, enter your guess for the value of the correlation coefficient for this scatterplot, and press Enter.
2. Second Guess.
Describe how close you were and what adjustments you might make in your thinking.
Solution.
Results will vary.
3. Ten Trials.
Repeat this process for a total of 10 scatterplots (you do not need to record your results but you should try to learn from the reveal of the actual values as you make your guesses). Do you think your guessing ability improved by the last scatterplot? Explain.
Solution.
Results will vary.
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Check the Track Performance box. The first graph is “Guess vs. Actual” graph with the (\(y = x\)) line shown.
4. Guess vs Actual.
Describe the behavior of the relationship between your guesses and the actual values of the correlation coefficients. Is there a strong correlation between your guesses and the actual values? Does this mean you are a good guesser? Explain.
Solution.
Results will vary.
5. Error vs Actual.
The next graph is the “Error vs. Actual” graph. Describe the behavior of the relationship between your errors and the actual values of the correlation coefficients. Were some correlation coefficients easier for you to guess than others? Use this graph to justify your answer.
Solution.
Results will vary.
6. Error vs Trial.
The last graph is the “Error vs. Trial” graph. Describe the behavior of the relationship between your errors and the order in which you saw the graphs. Did your ability seem to improve over time? Use this graph to justify your answer.
Solution.
Results will vary.
7. Perfect Guesser Thought Experiment.
Suppose you guessed every value correctly; what would be the value of the correlation coefficient between your guesses and the actual correlations?
Solution.
one (perfect linear relationship: guess = actual)
8. Systematic Offset Thought Experiment.
Suppose each of your guesses was too high by 0.2 from the actual value of the correlation coefficient. What would be the value of the correlation coefficient between your guesses and the actual correlations?
Solution.
one (perfect linear relationship: guess = actual + .2)
9. Interpretation Caveat.
Does a correlation coefficient equal to 1 necessarily imply you are a good guesser? Explain.
Solution.
Not necessarily. As shown in Question 8, every guess could be wrong but still lead to an \(r\) of 1.
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